I receive occasional emails from parents interested in buying their son/daughter a new saxophone. These often come with a link to an alto saxophone that is $250 or less made by brands such as Allora, Etude, Bundy, etc. Do not waste money on such junk.
Buying a saxophone is kind of like buying a car: if you buy something that's inexpensive, you'll end up paying its value three-fold in repairs. Cheaper saxophones are made of very soft brass, which means that their sound quality is poor and they break easily. Soft brass bends quite easily, which requires constant repair that doesn't hold up for very long. Needless to say, if the equipment is terrible, you're going to sound terrible.
Factors to consider: commitment level and budget
Beginners - Most beginners play on a Yamaha YAS-23 or a Selmer AS500, which are decent for young players just learning the ropes.
If the student wants to make a more serious commitment to music and plans to play into high school, consider getting an intermediate model. A quality intermediate will last through middle school and high school if it is taken care of, so it's well worth the investment to get something that will last several years. I play Selmer but I also highly recommend Yamaha saxophones. They are well-built and dependent with beautiful sound. The YAS-62 is particularly great, and if you can find one used, it would be a good investment. Yamaha's hold their value if you needed to sell it down the road. I'd also look at Buffet-Crampon 400 Series, Selmer Super Action 80 Series II, and Yanagisawa 901.
What's your budget? What can you reasonably afford without breaking the bank, keeping in mind that most families have to save up over time before purchasing an instrument? Again, remember you're paying for quality: precise manufacturing and quality pads, keywork, brass, lacquer, etc. matter!!
Some general tips:
1. Don't EVER bother with the "MSRP" price. When you see an MSRP price, it's an arbitrary list price that no one, and I mean no one, actually sells the saxophone for. I think it's a marketing trick to present the "suggested retail" next to the actual selling price to make the dealer look good.
2. Don't be afraid to buy used. Used saxophones with a couple scratches and normal wear-and-tear play just as nicely as new ones for several hundred dollars less.
3. Finally, even if you're not ready to purchase a saxophone, invest in a good mouthpiece. Selmer C-star and Vandoren AL3 are worth their weight in gold.